A Visual Tracking Study and A Proposal of Modifications

On-line visual tracking of a specified target in motion throughout frames of video clips faces challenges in robust identification of the target in the current frame based on the past frames. Three approaches for tracking the target image patch are described and compared. These approaches utilize particle filtering and principal component analysis (PCA) to identify the most likely location of the target in the current frame and a low dimensional subspace representation of the patches of images to be kept as the templates in the dictionary for the identification. By using a combination of methods and compare the result of each, a new model based is proposed. The goal is to achieve a more robust and accurate tracking of a target throughout the video and continue updating the identification templates to adapt the target changes, such as apparences in lighting, angle, scale and occlusions. The challenges in tracking are to introduction of the "right" templates into the identification templates in the dictionary and identify the most accurate particle image patch while tracking the target with the right tracking patch scaling. The first approach considered and on which the structure of the visual tracker is based is the "Incremental Learning for Robust Visual Tracking" by D. Ross et al., which is a computationally fast tracker that utilizes a method of low dimensional subspace for the identification template dictionary and incremental PCA for its tracking. The tracker has a simple rule in accepting the patches of images to be in the identification template dictionary after the image patch has gone through a singular value decomposition (SVD), where it eliminates singular values are smaller than $10^{-6}$ of the sum of squared sinuglar values and the corresponding bases are also eliminated. This elimination scheme has very limited robustness in tracking, therefore, more selective processes in accepting identification templates in the dictionary are explored and introduced on top of the existing method in comparison and to address the challenges in on-line video tracking. The second approach is the "Least Soft-Threshold Squares Tracking" proposed by D. Wang et al. solves the least soft-threshold squares distance problem to identify the distances of the particles to the templates in the dictionary, which greatly improves the tracking accuracy. This method is also computationally cheap in comparison to the first approach, and its accuracy is also better than the first approach, but it would sometimes fail to track in some applications. Finally, the third approach reviewed is the "Robust Visual Tracking and Vehicle Classification via Sparse Representation" by X. Mei et al. is to weight each particles when selecting the most likely target patch so the best patch has a highest weighted probability which ensures it being selected and introduced to the template dictionary. This approach performs well in comparison to the first and the second approaches in tracking accuracy and robustness, but this approach is extremely computationally expensive. Three new components are proposed in an effort to mitigate some of the limitations that the three approaches exhibit. One such component is to simply reject the image patches that exhibit too great of difference to the current template dictionary, which resulted in improved tracking robustness. This method is computationally cheap and easy to implement. Another component introduced is a second set of dictionary that is composed of admitted image patches, which is used for tracking when the image patches appears to be too dissimilar to the dictionary with low dimensional representation. It is expected that with more well defined and stronger features, it forces the tracking to identify the target. Finally, the third component introduced is the to prevent shrinkage of the target boundary box by weighting the particles drawn with the ratio of area change so that more weight is placed on particles with less arial change. This increases the likelihood of recovering the target again if tracking loses the target, and instead of shrinking the boundary box, the tracking is biased to staying with the image patch of the same size. The resulting performance of the proposed tracking scheme has not been noticeably improved, part of the reason is because the metrics available to identify a noisy image patch from the good image patches are not always indicative of the noisy-good image patch divide

Sparse learning of stochastic dynamic equations

With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems from simulation data. In this study, we extend SINDy to stochastic dynamical systems, which are frequently used to model biophysical processes. We prove the asymptotic correctness of stochastics SINDy in the infinite data limit, both in the original and projected variables. We discuss algorithms to solve the sparse regression problem arising from the practical implementation of SINDy, and show that cross validation is an essential tool to determine the right level of sparsity. We demonstrate the proposed methodology on two test systems, namely, the diffusion in a one-dimensional potential, and the projected dynamics of a two-dimensional diffusion process

Constrained Overcomplete Analysis Operator Learning for Cosparse Signal Modelling

We consider the problem of learning a low-dimensional signal model from a collection of training samples. The mainstream approach would be to learn an overcomplete dictionary to provide good approximations of the training samples using sparse synthesis coefficients. This famous sparse model has a less well known counterpart, in analysis form, called the cosparse analysis model. In this new model, signals are characterised by their parsimony in a transformed domain using an overcomplete (linear) analysis operator. We propose to learn an analysis operator from a training corpus using a constrained optimisation framework based on L1 optimisation. The reason for introducing a constraint in the optimisation framework is to exclude trivial solutions. Although there is no final answer here for which constraint is the most relevant constraint, we investigate some conventional constraints in the model adaptation field and use the uniformly normalised tight frame (UNTF) for this purpose. We then derive a practical learning algorithm, based on projected subgradients and Douglas-Rachford splitting technique, and demonstrate its ability to robustly recover a ground truth analysis operator, when provided with a clean training set, of sufficient size. We also find an analysis operator for images, using some noisy cosparse signals, which is indeed a more realistic experiment. As the derived optimisation problem is not a convex program, we often find a local minimum using such variational methods. Some local optimality conditions are derived for two different settings, providing preliminary theoretical support for the well-posedness of the learning problem under appropriate conditions.Comment: 29 pages, 13 figures, accepted to be published in TS

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

An interactive two-dimensional approach to query aspects rewriting in systematic reviews. IMS unipd at CLEF eHealth task 2

International audienc

Compressive Sensing of Analog Signals Using Discrete Prolate Spheroidal Sequences

Compressive sensing (CS) has recently emerged as a framework for efficiently capturing signals that are sparse or compressible in an appropriate basis. While often motivated as an alternative to Nyquist-rate sampling, there remains a gap between the discrete, finite-dimensional CS framework and the problem of acquiring a continuous-time signal. In this paper, we attempt to bridge this gap by exploiting the Discrete Prolate Spheroidal Sequences (DPSS's), a collection of functions that trace back to the seminal work by Slepian, Landau, and Pollack on the effects of time-limiting and bandlimiting operations. DPSS's form a highly efficient basis for sampled bandlimited functions; by modulating and merging DPSS bases, we obtain a dictionary that offers high-quality sparse approximations for most sampled multiband signals. This multiband modulated DPSS dictionary can be readily incorporated into the CS framework. We provide theoretical guarantees and practical insight into the use of this dictionary for recovery of sampled multiband signals from compressive measurements